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A remark on a Theorem of J. G. Thompson

Bertram Huppert — 1998

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

An important theorem by J. G. Thompson says that a finite group G is p -nilpotent if the prime p divides all degrees (larger than 1) of irreducible characters of G . Unlike many other cases, this theorem does not allow a similar statement for conjugacy classes. For we construct solvable groups of arbitrary p -lenght, in which the lenght of any conjugacy class of non central elements is divisible by p .

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